# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(s(t_h4s_sums_sum(X2,X1),h4s_bools_cond(s(t_bool,X6),s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X2,t_h4s_sums_sum(X2,X1)),h4s_sums_inl),s(X2,X5))),s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(X1,X4)))))=s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X2,t_h4s_sums_sum(X2,X1)),h4s_sums_inl),s(X2,X3)))<=>(p(s(t_bool,X6))&s(X2,X3)=s(X2,X5))),file('i/f/sum/cond__sum__expand_c2', ch4s_sums_condu_u_sumu_u_expandu_c2)).
fof(27, axiom,![X8]:![X7]:![X24]:![X25]:~(s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X8,t_h4s_sums_sum(X7,X8)),h4s_sums_inr),s(X8,X24)))=s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X25)))),file('i/f/sum/cond__sum__expand_c2', ah4s_sums_INRu_u_nequ_u_INL)).
fof(29, axiom,![X8]:![X7]:![X4]:![X5]:(s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X5)))=s(t_h4s_sums_sum(X7,X8),happ(s(t_fun(X7,t_h4s_sums_sum(X7,X8)),h4s_sums_inl),s(X7,X4)))<=>s(X7,X5)=s(X7,X4)),file('i/f/sum/cond__sum__expand_c2', ah4s_sums_INLu_u_11)).
fof(37, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X10),s(X7,X9)))=s(X7,X9),file('i/f/sum/cond__sum__expand_c2', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(38, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X10),s(X7,X9)))=s(X7,X10),file('i/f/sum/cond__sum__expand_c2', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(55, axiom,~(p(s(t_bool,f))),file('i/f/sum/cond__sum__expand_c2', aHLu_FALSITY)).
fof(56, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/sum/cond__sum__expand_c2', aHLu_BOOLu_CASES)).
fof(58, axiom,(~(p(s(t_bool,t)))<=>p(s(t_bool,f))),file('i/f/sum/cond__sum__expand_c2', ah4s_bools_NOTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
